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We consider the problem of computing dynamic correlation functions of quantumintegrable models employing the thermodynamic form-factor approach.Specifically, we focus on correlations of local operators that conserve thenumber of particles and consider the 2-particle-hole contribution to theirtwo-point functions. With the method developed being generally applicable toany finite energy and entropy state, our primary focus is on the thermalstates. To exemplify this approach, we chose the Lieb-Liniger model and studythe leading contribution from 2-particle-hole excitations at small momenta tothe dynamic density-density correlation function. We also consider analogouscontributions to two-point functions of higher local conserved densities andcurrents present in integrable theories.

The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models